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<span class="kw">set </span><font color="Maroon" title="c10">f</font> = (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c11">g</font> = (<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font>) <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> (<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c12">h</font> = (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font>) <a href="quaterni.html#K2" title="QUATERNI:func.2">--&gt;</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font>);<br/>
<a NAME="E1:12_1_1"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font>) <a href="quaterni.html#K2" title="QUATERNI:func.2">--&gt;</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>)</span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font>) <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> (<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></span>;<br/>
<a NAME="E2:12_1_1"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font>) <a href="quaterni.html#K2" title="QUATERNI:func.2">--&gt;</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T1" target="_self" title="QUATERNI:th.1">Th1</a></span>;<br/>
<a NAME="E3:12_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font>) <a href="quaterni.html#K2" title="QUATERNI:func.2">--&gt;</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_1"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:12_1_1"/>
(<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font>) <a href="quaterni.html#K2" title="QUATERNI:func.2">--&gt;</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c5">z</font></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span>,<font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_1"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T4" title="RELSET_1:th.4">RELSET_1:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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